One-Loop StringScatteringAmplitudes as Iterated Eisenstein Integrals

Schlotterer, Oliver; Broedel , Johannes

doi:10.1007/978-3-030-04480-0_7

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One-Loop StringScatteringAmplitudes as Iterated Eisenstein Integrals

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Schlotterer, Oliver
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Schlotterer, O., & Broedel, J. (2019). One-Loop StringScatteringAmplitudes as Iterated Eisenstein Integrals. In J. Blümlein (Ed.), Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, Texts & Monographs in Symbolic Computation (pp. 133-159 ). Springer Nature Switzerland AG.

Cite as: http://hdl.handle.net/21.11116/0000-0003-A1CB-2

Abstract

In these proceedings we review and expand on the recent appearance of iterated integrals on an elliptic curve in string perturbation theory. We represent the low-energy expansion of one-loop open-string amplitudes at multiplicity four and five as iterated integrals over holomorphic Eisenstein series. The framework of elliptic multiple zeta values serves as a link between the punctured Riemann surfaces encoding string interactions and the iterated Eisenstein integrals in the final results. In the five-point setup, the treatment of kinematic poles is discussed explicitly.